Positive factors

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Akansha: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Wed Sep 01, 2010 10:04 amFollowed by: 20 members; Thanked: 1 times

by Akansha » Sun May 29, 2011 10:22 am

If integer n is > 1, is n = 2?
a. n has exactly 2 positive factors
b. The difference of any 2 distinct positive factors of n is odd

OA is B

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Source: Beat The GMAT — Data Sufficiency | Sun May 29, 2011 10:22 am

SoCan: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Sun May 15, 2011 9:19 amFollowed by: 1 member; Thanked: 18 times

by SoCan » Sun May 29, 2011 10:38 am

Akansha wrote:If integer n is > 1, is n = 2?
a. n has exactly 2 positive factors
b. The difference of any 2 distinct positive factors of n is odd

OA is B

1) n can be any prime number, by definition
2) n cannot be an odd number, because every odd number has 1 and itself as a factor, and the difference between these is always even. Except for 2, every even number has 2 and itself as a factor, and that difference is always even. Two only has two factors, 2 and 1, and that difference is odd.

B is sufficient.

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